Question: Simplify the following expression: $r = \dfrac{7}{2p} + \dfrac{1}{10p}$
Explanation: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $2p$ and $10p$ $\lcm(2p, 10p) = 10p$ $ r = \dfrac{5}{5} \cdot \dfrac{7}{2p} + \dfrac{1}{1} \cdot \dfrac{1}{10p} $ $r = \dfrac{35}{10p} + \dfrac{1}{10p}$ $r = \dfrac{35 +1}{10p}$ $r = \dfrac{36}{10p}$ Simplify the expression by dividing the numerator and denominator by 2: $r = \dfrac{18}{5p}$